Question says "Rule to estimate the percentage of PE ratios that fall between? ts08Homework 08: Problem 3Previous ProblemProblem ListNext Problem(1 point)blemsThe price-earnings (PE) ratios of a sample of stocks have a mean value of 10.5 and a standard deviation of 1.4. If the PE ratios have a bell shapeddistribution, use the 68-95-99.7 Rule to estimate the percentage of PE ratios that fall between:A. 7.7 and 13.3.Percentage = 53.3B. 6.3 and 14.7.Percentage =C. 9.1 and 11.9.Percentage =%3DNote: You can earn partial credit on this problem.Preview My AnswersSubmit AnswersYou have attempted this problem 5 times.185FEBSALLétvMacBook AirDIIDD8088810F8F9F4F5F6F7F3

Answered: The price-earnings (PE) ratios of a…

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Question says "Rule to estimate the percentage of PE ratios that fall between?

ts
08
Homework 08: Problem 3
Previous Problem
Problem List
Next Problem
(1 point)
blems
The price-earnings (PE) ratios of a sample of stocks have a mean value of 10.5 and a standard deviation of 1.4. If the PE ratios have a bell shaped
distribution, use the 68-95-99.7 Rule to estimate the percentage of PE ratios that fall between:
A. 7.7 and 13.3.
Percentage = 53.3
B. 6.3 and 14.7.
Percentage =
C. 9.1 and 11.9.
Percentage =
%3D
Note: You can earn partial credit on this problem.
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Expert Solution

Step 1

Given: Let X denotes the price-earnings such that X~N( $μ, σ^{2}$ ) where

Population mean, $μ = 10.5$

Population SD, $σ = 1.4$

Part a: Using the probability

$P (7.7 \leq X \leq 13.3) = P (\frac{7.7 - μ}{σ} \leq \frac{X - μ}{σ} \leq \frac{13.3 - μ}{σ}) = P (\frac{7.7 - 10.5}{1.4} \leq Z \leq \frac{13.3 - 10.5}{1.4}) = P (- 2 \leq Z \leq 2)$

by the empirical rule $P (- 2 \leq Z \leq 2) = 0.95$

Therefore, the required percentage is 95%.

Part b: Using the probability

$P (6.3 \leq X \leq 14.7) = P (\frac{6.3 - μ}{σ} \leq \frac{X - μ}{σ} \leq \frac{14.7 - μ}{σ}) = P (\frac{6.3 - 10.5}{1.4} \leq Z \leq \frac{14.7 - 10.5}{1.4}) = P (- 3 \leq Z \leq 3)$

by the empirical rule $P (- 3 \leq Z \leq 3) = 0.997$

Therefore, the required percentage is 99.7%.

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